IDENTIFYING THE FINITE DIMENSIONALITY OF CURVE TIME SERIES
IDENTIFYING THE FINITE DIMENSIONALITY OF CURVE TIME SERIES
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DOI：
10.1214/10-aos819
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发表时间：
2010-12-01
影响因子：
4.5
通讯作者：
Ziegelmann, Flavio
中科院分区：
文献类型：
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作者：
Bathia, Neil;Yao, Qiwei;Ziegelmann, Flavio
曲线时间序列框架提供了一种方便的工具，可以将一些非静态特征纳入静态设置。提出了一种新的基于不同曲线间动态相关性的曲线时间序列维度识别方法。我们方法的实际实现归结为有限维矩阵的特征分析。此外，维度的确定等价于矩阵的非零本征值的识别，这是我们通过一些Bootstrap检验来实现的。研究了该方法的渐近性质。特别地，我们的零本征值估计具有较快的收敛速度n，而非零本征值的估计收敛于标准根n-率。用模拟数据集和真实数据集说明了所提出的方法。
The curve time series framework provides a convenient vehicle to accommodate some nonstationary features into a stationary setup. We propose a new method to identify the dimensionality of curve time series based on the dynamical dependence across different curves. The practical implementation of our method boils down to an eigenanalysis of a finite-dimensional matrix. Furthermore, the determination of the dimensionality is equivalent to the identification of the nonzero eigenvalues of the matrix, which we carry out in terms of some bootstrap tests. Asymptotic properties of the proposed method are investigated. In particular, our estimators for zero-eigenvalues enjoy the fast convergence rate n while the estimators for nonzero eigenvalues converge at the standard root n-rate. The proposed methodology is illustrated with both simulated and real data sets.